Looking at the front page of Propublica right now and it's just a straight up checklist of stories that people of a certain ideology believe. There's no opposing ideas or viewpoints present. They only run stories that the people reading it expect to read.
One test I came up with recently is that if a source doesn't run stories that I disagree with, if they only have stories which I nod along to and agree with, then that source is horribly biased. It isn't that they're "right", that they only run "right" stories, it's that they're horribly biased.
I don't think that test does much. The original point was that there's no such thing as objective news, but rather facts put into context.
If you're finding that context setting is consistent in its narrative, that's not a reason to recoil.
As an example, put yourself in a highly contentious context of a historical situation - say the apartheid in South Africa. If you found a newspaper that always took a position counter to the white south African government, you would have found a good newspaper.
That doesn't always work, but neither does a simple test like you've deviced.
One test I came up with recently is that if a source doesn't run stories that I disagree with, if they only have stories which I nod along to and agree with, then that source is horribly biased. It isn't that they're "right", that they only run "right" stories, it's that they're horribly biased.